The existence of trapped annular pressure and wellhead movement caused by downhole temperatures and stresses is known in the industry. In conventional well planning and completion design, engineers are challenged by well operations conducted above the end of the operating string (e.g., a workstring, tubing, etc.), which require accurate thermal, pressure, and stress estimation, especially in stage-by-stage hydraulic fracturing operations. In such operations, the scenarios become complex due to the use of plugs in the string, as well as packers in the annulus, at the operation depth (e.g., fracturing, injection perforation, or circulation depth), which result in isolated regions inside the string and/or in the annulus spaces. The wellbore components (fluids, casing, tubing, cements, etc.) have different thermal and stress responses in the regions above and below the plug and packers.
To date, however, conventional analysis techniques have only considered the thermal and stress responses below the end of the string, while failing to consider the thermal and stress responses above the end of the string. Therefore, current attempts have failed to provide the most accurate data for the complicated thermal, pressure, and stress behaviors on the wellbore and strings necessary for accurate and optimal tubular and completion designs, especially when there are a sequence of multiple operations performed step-by-step at different depths.